Sensitivity and uncertainty analysis for predicted soil test phosphorus using the APLE model

The long-term application of inorganic fertilizer and animal manure to agricultural fields has resulted in soil test P (STP) concentrations that greatly exceed the agronomic critical level in many areas of the world. This build-up of soil P, often referred to as legacy P, can increase the risk of P being mobilized during runoff and leaching events, even years or decades after P inputs have decreased or ceased. If this mobilized P reaches P-limited surface waters, eutrophication can result, leading to serious water quality problems that can adversely impact the environment, human health, and recreational activities. Due to the cost and effort involved in soil, manure, and runoff sampling and testing, as well as implementation of best management practices, nutrient management policies and strategies are often guided by computer model predictions. However, computer model predictions are inherently uncertain, thus it is important to account for this uncertainty when interpreting modeling data and using modeling results to guide decision making

In this study we conducted a sensitivity and uncertainty analysis using the Annual P Loss Estimator (APLE) model focusing on model predictions of STP. We calculated and evaluated the sensitivity coefficients of predicted STP and changes in STP using 1- and 10-yr simulations with and without P application. We also compared two methods for estimating prediction uncertainties: first-order variance approximation (FOVA) and Monte Carlo simulation (MCS). Finally, we compared uncertainties in APLE-predicted STP to uncertainties in measured STP collected from multiple sites in Maryland under different manuring and cropping treatments. Results from our sensitivity analysis showed that predicted STP and changes in STP for 1-yr simulations without P inputs were most sensitive to initial STP whereas model STP predictions were most sensitive to manure and fertilizer application rates when sensitivity analyses included P inputs. For the 10-yr simulations without P application inputs, the range in sensitivity coefficients for crop uptake and precipitation were much greater than for the 1-yr simulations. Prediction uncertainties from FOVA were comparable to those from MCS for model input uncertainties up to 50%. Using FOVA to calculate APLE STP prediction uncertainties using the Maryland data set, the mean measured STP for nearly all site years fell within the 95% confidence intervals of the STP prediction uncertainties. Our results provide users of APLE insight into what model inputs require the most careful measurement when using the model to predict changes in STP under conditions of P drawdown (i.e., no P application) or P buildup. Our results also demonstrate the importance of including model prediction uncertainties when estimating long-term drawdown of STP in agricultural fields.